Electrostatic potential of impurities in quantum wells

The method of images is used to calculate the electrostatic potential of an electric charge inside a double barrier structure. This potential is important for finding impurity energy levels in the quantum structure and has never been used before in exact form. The media were modeled by assigning different dielectric constants to the barriers and to the well. The highly doped contacts were assumed to have infinite dielectric constants. This method is based on calculating the Fourier transform parallel to the interfaces of the potential. This function can be obtained in closed form. The potential is then obtained by inverse Fourier transform. This integral is computationally more efficient to evaluate than the direct sum of Coulomb image terms